We pursue a statistical analysis comparing the acoustic features derived from subjects belonging to a pair of conditions. For this analysis, the mel-spec feature matrix computed for each audio file is averaged across the \(N_k\)  frames to obtain a \(192\times 1\)  dimensional average mel-spec feature vector. Subsequently, we obtain two populations of such feature vectors, one corresponding to each subject category.
We do a dimension-wise (across 192 dimensions) Mann-Whitney U test [1]} to statistically compare the feature values between two populations. The Mann-Whitney U test is a non-parametric test of the null hypothesis that, for randomly selected values of \(X\)  and \(Y\)  from two populations, the probability of \(X\)  being greater than \(Y\)  is equal to the probability of \(Y\)  being greater than \(X\) .
For summarizing the statistical significance across all the feature dimensions, we compute the harmonic mean of p-values (HMP) from the 192 p-values computed over each dimension of the average mel-spec feature vector. The HMP has been shown to be a robust measure for p-value summarization in high dimensional data analysis [2]}.
